WASHINGTON (CNN) -- The fight for Hispanic voters took center stage Tuesday as Sen. John McCain and Sen. Barack Obama took their campaigns to Washington to address the League of United Latin American Citizens.

It is the second of three major Hispanic and Latino organizations the two presidential candidates are addressing this summer and another sign of how important this voting bloc is in the race for the White House.

While the Arizona senator in his speech Tuesday morning failed to touch on specific immigration reform policies, McCain did reiterate his stance on the need for greater border security.

"I and many other colleagues twice attempted to pass comprehensive immigration legislation to fix our broken borders. ... Many Americans, with good cause, did not believe us when we said we would secure our borders, and so we failed in our efforts," he said. "We must prove to them that we can and will secure our borders first, while respecting the dignity and rights of citizens and legal residents of the United States.

"But we must not make the mistake of thinking that our responsibility to meet this challenge will end with that accomplishment. We have economic and humanitarian responsibilities as well, and they require no less dedication from us in meeting them," McCain added. Watch McCain speak Tuesday »

McCain also touched on America's need to compete in the global economy.

"The global economy is here to stay. We cannot build walls to foreign competition, and we shouldn't want to. When have Americans ever been afraid of competition? America is the biggest exporter, importer, producer, manufacturer, and innovator in the world. That's why I reject the false virtues of economic isolationism."

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Obama, the presumed Democratic nominee spoke later in the day. He focused much of his speech on blasting the Bush administration -- and McCain -- on immigration reform.

"I want to give Sen. McCain credit, because he used to buck his party on immigration. He fought for comprehensive immigration reform," Obama said. "I admired him for it. But when he started running for his party's nomination, he abandoned his courageous stance, and said that he wouldn't even support his own legislation if it came up for a vote."

Obama went on to say that Bush made "all kinds of promises to Latinos on the campaign trail, but failed to live up to them in the White House, and we can't afford that anymore."

"We need a president who isn't going to walk away from something as important as comprehensive reform when it becomes politically unpopular," he added.

"When 12 million people live in hiding in this country and hundreds of thousands of people cross our borders illegally each year; when companies hire undocumented workers instead of legal citizens to avoid paying overtime or to avoid a union; and a nursing mother is torn away from her baby by an immigration raid, that is a problem that all of us -- black, white and brown -- must solve as one nation," he said.

The speeches come on the same day a poll that says Americans are closely divided when it comes to building a fence along the U.S. border with Mexico.

In a CNN/Opinion Research Corp. poll, 52 percent of those polled favor building the 700-mile fence, while 47 percent oppose the idea.

The poll, conducted June 26-29, surveyed 1,026 Americans and carries a margin of error of plus or minus 3 percentage points.

"The American public is closely divided but the two parties are not," he said. "Fifty-eight percent of Democrats opposed a fence on the Mexican border, while 66 percent of Republicans favor one. Independents mildly favor a fence, by a 55 percent to 44 percent margin."

Though the issue of illegal immigration played a prominent role in the Republican presidential primary, it appears to be overshadowed heading into the general election by the nation's economic woes, the war in Iraq and other issues.

A recent CNN/Opinion Research Corp. poll showed Americans ranked the issue ninth in importance to their vote in November.

Obama and McCain both voted last year to authorize the building of the fence. The border fence carries a price of more than $3 billion.

Both senators have made a large effort to attract Latino voters, most recently when the two spoke at the annual conference of NALEO, the National Association of Latino Elected and Appointed Officials on June 28 in Washington.

A week later, McCain released a Spanish radio ad on July 4, voiced by McCain's U.S. Naval Academy roommate Frank Gamboa. "It seems to me that the other candidate has just discovered the importance of the Hispanic vote," Gamboa says in the ad, while playing up McCain's history with the Hispanic community. The ad is airing in Nevada and New Mexico.